Mathematics encompasses a wide variety of skills and concepts, which are related and often build on one another. The neurodevelopment functions of memory, language, attention, temporal-sequential ordering, higher-order cognition, and spatial ordering also play roles in learning mathematics and must work together for children to succeed in mathematics. Children must be able to use memory to recall rules and formulas and recognize patterns, use language to understand vocabulary, instructions, and to explain their thinking, and use sequential ordering to solve multi-step problems and use procedures. In addition, children must use spatial ordering to recognize symbols and deal with geometric forms. Given that math is cumulative in nature, it is, therefore, important to identify breakdowns and pattern recognition as early as possible, and children must be properly trained to identify broad themes and patterns in mathematics and transfer them within and across situations. Accordingly, there is a need in the art for specialized apparatus and methods useful in demonstrating mathematical breakdowns and patterns for the purpose of developing skills and concepts useful in mathematics learning.